Properties

Level $6$
Weight $0$
Character 6.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 13.2545279009 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+0.253620632\)
\(a_{6}=-0.408248290\) \(a_{7}=-0.920438122\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.179336869\)
\(a_{11}=-0.601271670\) \(a_{12}=+0.288675135\) \(a_{13}=+1.218836069\) \(a_{14}=+0.650848038\) \(a_{15}=+0.146427940\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.629906495\) \(a_{18}=-0.235702260\) \(a_{19}=-1.020566515\) \(a_{20}=+0.126810316\)
\(a_{21}=-0.531415198\) \(a_{22}=+0.425163275\) \(a_{23}=-1.902282141\) \(a_{24}=-0.204124145\) \(a_{25}=-0.935676575\)
\(a_{26}=-0.861847250\) \(a_{27}=+0.192450090\) \(a_{28}=-0.460219061\) \(a_{29}=+1.251858034\) \(a_{30}=-0.103540189\)
\(a_{31}=-1.335882834\) \(a_{32}=-0.176776696\) \(a_{33}=-0.347144359\) \(a_{34}=-0.445411149\) \(a_{35}=-0.233442099\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.084728249\) \(a_{38}=+0.721649503\) \(a_{39}=+0.703695333\) \(a_{40}=-0.089668434\)
\(a_{41}=-0.237709943\) \(a_{42}=+0.375767290\) \(a_{43}=-1.540889664\) \(a_{44}=-0.300635835\) \(a_{45}=+0.084540211\)
\(a_{46}=+1.345116601\) \(a_{47}=-1.390582358\) \(a_{48}=+0.144337567\) \(a_{49}=-0.152793663\) \(a_{50}=+0.661623251\)
\(a_{51}=+0.363676684\) \(a_{52}=+0.609418035\) \(a_{53}=-0.247682092\) \(a_{54}=-0.136082763\) \(a_{55}=-0.152494901\)
\(a_{56}=+0.325424019\) \(a_{57}=-0.589224352\) \(a_{58}=-0.885197305\) \(a_{59}=+0.916445871\) \(a_{60}=+0.073213970\)
\(a_{61}=-1.390579281\) \(a_{62}=+0.944611810\) \(a_{63}=-0.306812707\) \(a_{64}=+0.125000000\) \(a_{65}=+0.309121975\)
\(a_{66}=+0.245468131\) \(a_{67}=+0.188593531\) \(a_{68}=+0.314953248\) \(a_{69}=-1.098283106\) \(a_{70}=+0.165068491\)
\(a_{71}=+1.155632788\) \(a_{72}=-0.117851129\) \(a_{73}=+0.218702863\) \(a_{74}=+0.059911915\) \(a_{75}=-0.540213124\)
\(a_{76}=-0.510283247\) \(a_{77}=+0.553433375\) \(a_{78}=-0.497587746\) \(a_{79}=-1.741241363\) \(a_{80}=+0.063405158\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.168086313\) \(a_{83}=+1.118448678\) \(a_{84}=-0.265707599\) \(a_{85}=+0.159757283\)
\(a_{86}=+1.089573530\) \(a_{87}=+0.722760573\) \(a_{88}=+0.212581638\) \(a_{89}=+0.326314123\) \(a_{90}=-0.059778956\)
\(a_{91}=-1.121863183\) \(a_{92}=-0.951141070\) \(a_{93}=-0.771272314\) \(a_{94}=+0.983290215\) \(a_{95}=-0.258836725\)
\(a_{96}=-0.102062072\) \(a_{97}=-0.573530100\) \(a_{98}=+0.108041435\) \(a_{99}=-0.200423890\) \(a_{100}=-0.467838287\)

Showing 100 of 1000 available coefficients

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